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| 183_notes:grav_accel [2018/05/29 20:19] – hallstein | 183_notes:grav_accel [2021/02/05 00:02] (current) – [The Gravitational Force and the Momentum Principle] stumptyl |
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| $$\vec{a}_2 = -G\dfrac{m_1}{|\vec{r}|^2}\hat{r}$$ | $$\vec{a}_2 = -G\dfrac{m_1}{|\vec{r}|^2}\hat{r}$$ |
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| The resulting expression is the acceleration that object 2 experiences due to it's gravitational interaction with object 1. Notice that the acceleration of object 2 depends only on the mass of object 1 ($m_1$), and relative position of object 2 with respect to object 1 ($\vec{r}$). It also points towards object 1, which indicates that the object 2 is attracted (and will thus experience an acceleration along the line between object 1 and 2). | //__The resulting expression is the acceleration that object 2 experiences due to it's gravitational interaction with object 1__//. Notice that the acceleration of object 2 depends only on the mass of object 1 ($m_1$), and relative position of object 2 with respect to object 1 ($\vec{r}$). It also points towards object 1, which indicates that the object 2 is attracted (and will thus experience an acceleration along the line between object 1 and 2). |
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| So, in general: | So, __in general__: |
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| $$\vec{a} = -G\dfrac{m}{|\vec{r}|^2}\hat{r}$$ | $$\vec{a} = -G\dfrac{m}{|\vec{r}|^2}\hat{r}$$ |